Assume that shoes are produced in three countries: 30 percent in Korea, 40 perce
ID: 3209121 • Letter: A
Question
Assume that shoes are produced in three countries: 30 percent in Korea, 40 percent in New Zealand, and 30 percent in China. At the plant in each country, two types of shoes are made: racing shoes and training shoes. The production at each plant as allocated as shown in the table below. The shoes are randomly distributed to stores in the United States, and you purchase one pair from one of these stores.
Plant/Racing/Training
Korea/0.8/0.2
New Zeland/0.55/0.45
China/0.65/0.35
If you purchase a pair of training shoes selected at random, what is the probability that they were made in Korea?
Explanation / Answer
let probailty of training shoes =P(T)
and probabilty it is madse in Korea=P(K); in New Zealand=P(N) and in China =P(C)
therefore probabiltyof a a pair of training shoes P(T)=P(K)*P(T|K)+P(N)*P(T|N)+P(C)*P(T|C)
=0.3*0.2+0.4*0.45+0.3*0.35=0.345
hence probability that they were made in Korea,given you purchase a pair of training shoes
=P(K|T)=P(K)*P(T|K)/P(T) =0.3*0.2/0.345=0.1739